Question

3. A password is a sequence of letters (a–z) and digits (0–9). Find the number of passwords of length 10 under the constraints in (a), (b) or (c) (three separate problems).

Express your answer using factorials and integers, products and ratios of them, and/or sums of such things.

(a) There are 3 letters and 7 digits, and at most one ‘9’.

(b) There are 6 letters and 4 digits, and no digit occurs twice.

(c) No letters are used BUT the first four digits are not all the same AND the last four digits are not all the same, AND the 4th, 5th, 6th and 7th digits are not all the same.

Answer 1

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